Optic disc detection by earth mover's distance template matching

Abstract—This paper presents a method for the detection of OD in the retina which takes advantage of the powerful preprocessing techniques such as the contrast enhancement, Gabor wavelet transform for vessel segmentation, mathematical morphology and Earth Mover’s distance (EMD) as the matching process. The OD detection algorithm is based on matching the expected directional pattern of the retinal blood vessels. Vessel segmentation method produces segmentations by classifying each image pixel as vessel or nonvessel, based on the pixel’s feature vector. Feature vectors are composed of the pixel’s intensity and 2D Gabor wavelet transform responses taken at multiple scales. A simple matched filter is proposed to roughly match the direction of the vessels at the OD vicinity using the EMD. The minimum distance provides an estimate of the OD center coordinates. The method’s performance is evaluated on publicly available DRIVE and STARE databases. On the DRIVE database the OD center was detected correctly in all of the 40 images (100%) and on the STARE database the OD was detected correctly in 76 out of the 81 images, even in rather difficult pathological situations.

Keywords—Diabetic retinopathy, Earth Mover’s distance, Gabor wavelets, optic disc detection, retinal images

I. INTRODUCTION

HE retina is the inner-most and the important layer of the eye where the earliest pathological changes are seen. It is composed of various anatomical structures which indicate many diseases, such as hypertension, diabetic retinopathy and glaucoma. Retinopathy is one of the main causes of blindness in the working age population. Analysis of retinal images is considered essential for diagnosis and treatment of many diseases affecting the retina. These images must be accurately segmented to extract sensitive objects in the retina such as the blood vessel tree, the optic disc, the macula and the region between the optic disc (OD) and the macula.

Retinal or fundus images provide information about the blood supply system to the retina. The OD which in fundus images usually appears as a round region brighter than the surrounding is the image of the optic nerve and is the exit point of retinal nerve fibers from the eye and the entrance and exit point for retinal blood vessels. It consequently has a very different appearance to the rest of the retina, usually appearing as a bright, approximately circular region intersected by blood vessels (See Fig. 1(a)). Optic Disc detection is a reference to locate the various anatomical features in the

Fernando C. Monteiro is with the Polytechnic Institute of Braganc¸a, Campus Santa Apolónia, Apartado 1134, 5301-857 Bragança, Portugal. ( e- mail: monteiro@ipb.pt).

Vasco Cadavez is with the Mountain Research Center (CIMO), ESA - Polytechnic Institute of Braganc¸a, Campus Santa Apolónia, Apartado 1172, 5301-855 Braganc¸ a, Portugal. ( e-mail: vcadavez@ipb.pt).

retinal images and its location is quite important since many retinal pathologies may affect the optic nerve. Anatomical variation as well as refractive differences between eyes affect its apparent size. Since the OD may be easily confounded with large exudative lesions by image analysis techniques, its detection is also important to exclude it from the set of possible lesions. Although manual localization of the OD is sufficient, the process can be prohibitively cumbersome when dealing with large number of images. This has stimulated several research groups to develop algorithms for automatic localization of the OD [1].

OD localization methods can be classified into two main categories, appearance-based methods and vessel-based meth- ods. Appearance-based methods identify the location of the OD as the location of the brightest round object within the retinal image. Lalonde et al. [2]) implemented a Hausdorff- based template matching technique using edge maps, guided by pyramidal decomposition for large-scale object tracking. Zhu et al. [3] proposed a method based on edge detection and the Hough transform for the detection of circles in areas where the highest local maximum in the Hough space also meets the condition based on 90% of the reference intensity. In Li and Chutatape [4], the brightest 1% of image pixels were firstly clustered as candidate optic disc regions. The regions larger than a fixed area threshold were taken as candidate regions for the optic disc. Next, principal component analysis based on a training set of ten manually extracted optic discs, normalized for size and intensity, was used to select a single point in the candidate regions. Then, the location of the optic disc center was found by calculating the minimum distance between the original retinal image and its projection. These techniques, however, often fail on pathological images, where atypical pigmentation, therapeutic laser scars and a number of pathological features may be characterized by round shape and/or elevated brightness, e.g., large exudative lesions.

Vessel-based methods depend mainly upon extracting and analyzing the structure of the retinal vessels and defining the location of the OD as the point where all the retinal vessels radiate. In Hoover and Goldbaum [5], an original vessel segments fuzzy convergence algorithm was proposed to identify the position of the optic nerve image as the focal point of the blood vessel network. The method of Foracchia et al. [6] is based on a model of vessel orientation in the retina relative to the optic disc position. The model was fitted to the measured vessel directions using simulated annealing, the measurements being weighted by vessel calibre so that larger vessels have a greater influence on the result. Relying on matching the expected directional pattern of the retinal blood vessels in the vicinity of the OD, Youssif et al. [7] proposed a method to

Fernando C. Monteiro and Vasco Cadavez

Optic Disc Detection by Earth Mover’s

Distance Template Matching

T

detect the OD. A two-dimensional Gaussian matched filter was used to obtain a direction map of the segmented retinal vessels. The Gaussian matched filter was resized in four different sizes, and the difference between the output of the matched filter and the vessels’ directions was measured. The minimum difference was used to estimate the coordinates of the center of the OD.

In this work, a technique for OD detection is proposed. The new method can be classified as a vessel-based method in which the OD is considered the region where the main retinal vessels originate in a parabolic direction. This method takes advantage of the powerful preprocessing techniques such as the contrast enhancement, Gabor wavelet transform, mathematical morphology and Earth Mover’s distance for the matching pattern. The methods include the design of a bank of directionally sensitive Gabor filters for several values of the scale and elongation parameters as proposed by Soares et al. [8]. Forty images of the retina from the DRIVE database [9] and 81 images of the retina from the STARE database [5] were used to evaluate the performance of the method.

The rest of this paper is organized as follows. Section II describes the proposed OD detection technique. Experimental results are then described and discussed in Section III. Some concluding remarks are finally drawn in Section IV.

II. PROPOSED METHOD

This section presents the proposed OD detection technique. In particular, we divide this section into three subsections, which deal with the retinal image preprocessing, blood vessel segmentation, and OD detection, respectively.

A. Retinal Image Preprocessing

Retinal images need to be preprocessed before the OD detection. Several other works on the detection of retinal vessels have used the green channel only, however, as the proposed technique makes use of the brightness of the OD, the lightness component within the CIE-Lab colour space of a retinal image is first extracted (Fig. 1(a)). The CIE-Lab space allows us to work with just the luminance in an image without suffering from colour noise influence.

In order to reduce false detection of the border of the camera’s aperture, an iterative algorithm has been developed. We used the method proposed by Soares et al. [8]. Our intent is to remove the strong contrast between the retinal fundus and the region outside the aperture. The preprocessing algorithm starts with a region of interest (ROI) determined by the camera’s aperture and iteratively grows this ROI by replace each pixel value with the mean value of its eight neighbours inside the ROI. Finally, the ROI is expanded by inclusion of this altered set of pixels. This process is repeated and can be seen as artificially increasing the ROI, as shown in Fig. 1(b). Without some type of colour normalization for the back- ground pigmentation, the large variation in natural retinal pigmentation across the population confounds discrimination of the relatively small variations between the different lesion types. As the contrast between the blood vessels (foreground) and the retinal tissue (background) is generally poor in the retinal images, an effective technique called contrast-limited

(a) (b)

Fig. 1 Fundus image extension for removing undesired border effects. (a) Lightness of STARE’s retinal image in CIE-Lab colour

space. (b) Image with extended border.

(a) (b)

Fig. 2 Retinal image preprocessing.(a) Result of contrast enhancement with CLAHE. (b) Inverted image were vessels appear

brighter than the background

adaptive histogram equalization (CLAHE) is used for contrast enhancement by limiting the maximum slope in the transformation function. Instead of applying the histogram equalization on the entire image, it is applied only on small non-overlapping regions in the image. Then, the neighbouring tiles are combined using bilinear interpolation to reduce induced boundaries. Fig. 2(a) shows the contrast enhancement produced by CLAHE approach.

The contrast enhanced image is inverted before the application of the wavelet transform to it, so that the vessels appear brighter than the background as showed in Fig. 2(b).

B. Blood Vessel Segmentation

In many applications of image processing in ophthalmology, the most important step is to detect the blood vessels in the retina. Many algorithms have been developed for extracting the vascular structure from fundus images [5], [6], [8].

We propose image processing techniques to detect blood vessels in images of the retina based upon Gabor wavelet [8] which takes advantage of the fact that blood vessels are elongated, piecewise-linear or curvilinear structures with a preferred orientation. This approach produces segmentations by classifying each image pixel as vessel or nonvessel, based on the pixel’s feature vector. Feature vectors are composed of the pixel’s intensity and 2D Gabor wavelet transform responses taken at multiple scales.

Gabor wavelets are sinusoidally modulated Gaussian functions that have optimal localization in both the frequency and space domains, thus allowing noise filtering and vessel enhancement in a single step. The wavelet is capable of

detecting directional structures and of being tuned to specific frequencies, which is especially important for filtering out the background noise present in retinal images.

The notation and definitions in this section follow [8]. The continuous wavelet transform Tψ

(

)

in terms of the scalar product of f with the transformed wavelet ψb_{, ,a}θ . This transform can be easily implemented

using the fast Fourier transform algorithm and the equivalent Fourier definition of the wavelet transform:

(

)

(

) (

) ( )

T_ψ bθ a =C_ψ− a

∫

where Cψ, , , ,ψ bθ a denote the normalizing constant,

analyz-ing wavelet, the translation vector, the rotation angle, and the dilation parameter (also known as scale), respectively. ψ* denotes the complex conjugate of ψ and the hat (i.e., ψˆ*and

ˆf denotes a Fourier transform. The Gabor wavelet is actually a complex exponential modulated Gaussian, where k is a vector that defines the frequency of the complex exponential.

For each pixel position and considered scale value, we are interested in the response with maximum modulus over all possible orientations, i.e.,

(

)

(

)

M_ψ a T_ψ a

θ θ

=

b b (2)

The Gabor wavelet transform is computed for spanning from 0 up to 170 degrees at steps of 10 degrees. The maximum moduli of the wavelet transform over all angles for various scales are then taken as pixel features. The filter elongation parameter was set to ε = and 4 k₀ =

[ ]

Fig. 3 shows the results obtained using scale values of

{ }

a = pixels. The result in Fig. 3(a) indicates that the filters have detected only the edges of the thick vessels, with poor response along their center-lines. On the contrary, the result in Fig. 3(b) shows that, while the thick vessels have been detected well, some of the thinner vessels have not been detected. The results indicate the need for multiscale or mul- tiresolution filtering and analysis, which is easily facilitated by the proposed design of the Gabor wavelet.

In the tests performed, the scale parameter is varied as

{

}

a = pixels. These scales were chosen as to span the possible widths of vessels throughout the images, so that all vessels could be detected. Illustrative segmentation results for a pair of images from the STARE dataset, along with the manual segmentations, is shown in Fig. 4.

C. Optic Disc Detection

A distinguishing feature of the optic disc is that it is the region of convergence for the blood vessel network. The shape, colour, and size of the OD showed large variance especially in the presence of retinopathies, and therefore, detection methods based on these properties were shown to be weak, and impractical.

As stated by Hoover et al. [5], ”A matched filter describes the expected appearance of a desired signal, for purposes of comparative modeling”. Thus, in order to detect the OD, a

(a) (b)

Fig. 3. Maximum modulus response of Gabor wavelet transform over 18 Gabor filters with ε=4and k0=[ ]0, 3 . (a) Scale value of a= pixels. 2

(b) Scale value of a= pixels. 5

(a) (b)

Fig. 4 Blood vessel segmentation (a) Two images from STARE database. (b) Manual segmentations

simple vessel’s matched filter is proposed to roughly match the vessels at the OD vicinity.

By visual inspection of retinal fundus images, it appears that a common vascular pattern is present among images: the main vessels originate from the OD follow a specific course that can be geometrically modeled as two opposite semi-parabolas, with a common vertex inside the OD. The distance between the pattern and the thinned vessel map is obtained using the Earth Mover’s distance (EMD) approach.

Rubner et al. [10] introduced the EMD to measure per- ceptual similarity between images for the purpose of image retrieval. EMD evaluates dissimilarity between two distribu- tions or signatures in some feature space where a distance measure is given. Intuitively, given two distributions, one can be seen as a mass of earth properly spread in space, the other as a collection of holes. Then, the EMD measures the least amount of work needed to fill the holes with earth. Here, a unit of work corresponds to transporting a unit of earth by a unit of ground distance. The EMD between two distributions is given by the minimal sum of costs incurred to move all the individual points between the signatures.

Let

{

(

)

(

)

}

1

1, p ,..., m, pm

P= p w p w be the first signature with

m pixels, where p is the pixel representative and i w is pi

the weight of the pixel; the second signature with n pixels is

represented by

{

(

)

(

)

}

1

1, q ,..., n, qn

Q= q w q w , and D=   the  d_ij

distance matrix where d is the distance between two _ij

points’ image coordinatesp_iandq . The flow _j f is the ij amount of weight moved fromp_itoq . The EMD is defined _j

as the work normalized by the total flow f , that minimizes _ij

the overall cost:

(

)

∑∑

∑∑

As pointed by Rubner et al. [10], if two weighted point sets have unequal total weights, EMD is not a true metric. It is desirable for robust matching to allow point sets with varying total weights and cardinalities. In order to embed two sets of contour features with different total weights, we divide the blood vessel image in several overlapping tiles and simulate equal weights by adding the appropriate number of points, to the lower weight set, with a penalty of maximal distance. As a measure of distance for the EMD, we use

1 i j p q ij d e α − − = − (4)

where p_i −q_j is the Euclidean distance between p_i and q_j

and α is used in order to accept some deformation of the matching pattern. The exponential map limits the effect of large distances, which otherwise dominate the result.

To reduce the computational burden, pattern matching is applied only to candidate pixels picked from the fundus image [7]. The retinal image is smoothed using the bilateral filter [11] that combines geometric closeness and photometric similarity. Fig. 5(a) shows the filtered retinal image of Fig. 2.

The binary vessel/nonvessel image is thinned by applying a morphologic algorithm that reduces all objects in the binary image to the pixel dimension keeping in the new image only the central pixels of the vessels. The number of candidates is reduced by considering only the ones which are within a 41 41× square centered on each of the highest 4% intensity pixels in the image as showed in Fig. 5(b).

III. EXPERIMENTAL RESULTS

This section presents experimental results. The two public datasets used are first described. The performance of the pro- posed OD detection method is then presented and discussed.

A. Data Description

The proposed method was tested with fundus images of the retina from two public datasets. In particular, the first dataset is Digital Retinal Images for Vessel Extraction (DRIVE) database that is composed of 40 images (seven of which present pathology) obtained from a diabetic retinopathy screening program. The images are acquired using a Canon CR5 3CCD camera at 45º field of view, compressed in JPEG

(a) (b)

Fig. 5 OD center candidates. (a) Retinal image smoothed by bilateral filtering. (b) Final OD center candidates

format of size 565×584 pixels, eight bits per colour channel and have a FOV of approximately 540 pixels in diameter. The 40 images were divided into two sets, a test set and a training set, each containing 20 images. The second one is Structured Analysis of the Retina (STARE) database, which consists of 81 images captured by a TopCon TRV-50 fundus camera at 35º FOV. The images were digitized to 700×605 pixels, eight bits per colour channel. The FOV in the images are approximately 600 pixels in diameter. The dataset is composed of 50 images containing pathological lesions of various types and severity and 31 images of healthy retina. It is created for benchmarking OD detection and is much more challenging compared with the DRIVE dataset.

B. OD detection results

As proposed also in [6],[7], the OD position was considered correctly detected if the estimated coordinates were inside the contour of the OD, i.e., within 60 pixels of its center, as manually identified for ground truth. The method was able to correctly detect the OD in 116 out of 121 images.

Fig. 6 shows some illustrative OD detection results. Examples of highly pathological images in which the OD was successfully identified are shown in the second row of Fig. 6.

C. Discussion

Although we do not show any images from DRIVE dataset, we have tested the proposed technique in that dataset with a success rate of 100% (the OD center was detected correctly in all of the 40 images).

Results on the 81 normal and pathological images of the STARE project were satisfying, despite the presence of heavily confounding features in many of them. For example, in the im- ages shown in Fig. 6, middle, the retina covered by extensive retinal lesions, either dark hemorrhages or bright exudates, and would have proved impossible to be detected by techniques based only on brightness or shape. Thanks to the fusion information from retinal vessel geometry and brightness, the proposed technique was able to correctly identify the position of OD also in these very difficult images. In the images of Fig. 6, bottom, the proposed method fails due mainly to severe hemorrhages which make the blood vessels undefined and darken the OD pixels. Also, the method did not perform well for very large variations in lighting

Fig. 6 OD detection examples within STARE images without pathologies. The second row

shows the five retinal images that suffer from

throughout an image, but this occurred out of the 121 tested from both databases bottom row of Fig. 6).

Finally, the proposed technique still has First, the proposed pattern matching is based tion that there are visible blood vessels drawback of our approach is that it is based that the OD is more or less brighter than retinal pixels and, therefore, cannot handle whose OD is even darker than the surrounding pi

The proposed method achieved a success the OD was detected correctly in 116 out

contained in the DRIVE and STARE databases). In the evaluation of our technique is close to

[6],[7] that rely on the retinal blood vessel. IV. CONCLUSION

In this paper, a simple and computationally e algorithm for automatic OD detection has been presented. The proposed algorithm takes advantage of

preprocessing techniques such as the contrast Gabor wavelet transform, mathematical morphology Mover’s distance as the matching process.

vessel extraction procedure is a necessary technique, and the performances of this the correct positioning of the OD.

ARE dataset (black mark (x) represents the estimated OD w shows five retinal images that suffer from different types from different types of retinal lesions and imaging artifacts

for only one image databases (fifth image of the has several limitations. based on the assump- essels on OD. Another based on the assumption brighter than the surrounding handle retinal images surrounding pixels.

success rate of 95.9% (i.e., out of the 121 images databases). In addition, to that of the methods essel.

computationally efficient for automatic OD detection has been presented. The antage of the powerful contrast enhancement, morphology and Earth process. The availability of a necessary prerequisite for our step directly affects

REFERENCES

[1] R. Winder, P. Morrow, I. McRitchie, J. Bailie, and P. Hart, “Algorithms for digital image processing in diabetic retinopathy,”

Medical Imaging and Graphics

[2] M. Lalonde, M. Beaulieu, and L. Gagnon, “Fast and robust optic disk detection using pyramidal decomposition and hausdorff

matching,” IEEE Transactions on Medical Imaging 1193–1200, 2001.

[3] X. Zhu, R. Rangayyan, and A. Ells, “Detection of the optic nerve head in fundus images of the retina using the hough transform for circles,” Journal of Digital Imaging, vol. 23, no. 3, pp. 332

[4] H. Li and O. Chutatape, “Automated feature extraction in color retinal images by a model based approach,”

Engineering, vol. 51, no. 2, pp. 246

[5] A. Hoover and M. Goldbaum, “Locating the optic nerve in a retinal image using the fuzzy convergence of the blood vessels,”

actions on Medical Imaging, vol. 22, no. 8, pp. 951

[6] M. Foracchia, E. Grisan, and A. Ruggeri, “Detection of optic disc in retinal images by means of a geometrical model of vessel structure,” IEEE Trans. on Medical Imaging

[7] A. Youssif, A. Ghalwash, and A. Ghoneim, “Optic disc detection from normalized digital fundus images by means of a vessels’ direction matched filter,” IEEE Transactions on Medical Imaging

pp. 11–18, 2008.

[8] J. Soares, J. Leandro, R. C. Jr., H. Jelinek, and M. Cree, “Retinal vessel segmentation using the 2-d gabor wavelet and supervised classification,” IEEE Trans. on Medical Imaging

[9] J. Staal, M. Abramoff, M. Niemeijer, M.

Ginneken, “Ridge-based vessel segmentation in color images of the retina,” IEEE Trans. on Medical Imaging

2004.

[10] Y. Rubner, C. Tomasi, and L. Guibas, “The earth mover’s distance as a metric for image retrieval,” International Journal of Computer Vision vol. 40, no. 2, pp. 99–121, 2000.

[11] C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in International Conference on Computer Vision

India, 1998, pp. 839 –846.

center). The first row shows retinal types of retinal lesions. The third row

where the proposed method fails

EFERENCES

R. Winder, P. Morrow, I. McRitchie, J. Bailie, and P. Hart, “Algorithms for digital image processing in diabetic retinopathy,” Computerized Medical Imaging and Graphics, vol. 33, no. 8, pp. 608–622, 2019. M. Lalonde, M. Beaulieu, and L. Gagnon, “Fast and robust optic disk detection using pyramidal decomposition and hausdorff-based template IEEE Transactions on Medical Imaging, vol. 20, no. 11, pp. Ells, “Detection of the optic nerve head in fundus images of the retina using the hough transform for circles,”

, vol. 23, no. 3, pp. 332–341, 2010.

H. Li and O. Chutatape, “Automated feature extraction in color retinal s by a model based approach,” IEEE Transactions on Biomedical

, vol. 51, no. 2, pp. 246–254, 2004.

A. Hoover and M. Goldbaum, “Locating the optic nerve in a retinal image using the fuzzy convergence of the blood vessels,” IEEE Trans-

, vol. 22, no. 8, pp. 951–958, 2003. M. Foracchia, E. Grisan, and A. Ruggeri, “Detection of optic disc in retinal images by means of a geometrical model of vessel structure,” IEEE Trans. on Medical Imaging, vol. 23, no. 10, pp. 1189–1195, 2004. A. Youssif, A. Ghalwash, and A. Ghoneim, “Optic disc detection from normalized digital fundus images by means of a vessels’ direction IEEE Transactions on Medical Imaging, vol. 27, no. 1, ares, J. Leandro, R. C. Jr., H. Jelinek, and M. Cree, “Retinal vessel d gabor wavelet and supervised classification,” IEEE Trans. on Medical Imaging, vol. 25, no. 9, pp. 1214–1222, 2006. J. Staal, M. Abramoff, M. Niemeijer, M. Viergever, and B. van

based vessel segmentation in color images of the IEEE Trans. on Medical Imaging, vol. 23, no. 4, pp. 501–509, Y. Rubner, C. Tomasi, and L. Guibas, “The earth mover’s distance as a International Journal of Computer Vision, 121, 2000.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color International Conference on Computer Vision, Bombay,